Increasing the domain of locality by using tree-adjoining-grammars (TAG) encourages some researchers to use it as a modeling formalism in their language application. But parsing with a rich grammar like TAG faces two main obstacles: low parsing speed and a lot of ambiguous syntactical parses. We uses an idea of the shallow parsing based on a statistical approach in TAG formalism, named supertagging, which enhanced the standard POS tags in order to employ the syntactical information about the sentence. In this paper, an error-driven method in order to approaching a full parse from the partial parses based on TAG formalism is presented. These partial parses are basically resulted from supertagger which is followed by a simple heuristic based light parser named light weight dependency analyzer (LDA). Like other error driven methods, the process of generation the deep parses can be divided into two different phases: error detection and error correction, which in each phase, different completion heuristics applied on the partial parses. The experiments on Penn Treebank show considerable improvements in the parsing time and disambiguation process.